Allow me to explain as to why I support the Empire, and why I believe it is the best option for Skyrim (Keep in mind that I will be repeating what others before me have said):
1. The Empire provides resources to Skyrim - It is widely known that Skyrim has little to boast about regarding their farming. Very few farms in Skyrim are successful, due to the climate, with exceptions being Rorikstead, and I believe a couple farms throughout the Rift and Eastmarch. Skyrim, as a whole, cannot hope to live off that little food. In fact, that's barely enough to feed the remaining husk that is Winterhold. And not just that, but Skyrim doesn't contain large amounts of valuable mining material. They can boast of silver, and the occasional conundrum and, even rarer, ebony, but the majority of minerals found in Skyrim is iron ore. As said, that's not enough for armor creation. The Empire provides all of these things, and has been for many, many years. Breaking off from this would be foolish and counterproductive.
2. The Empire is the morally-good option - In the end, depending on the amount of lore, and from who's perspective it's being told from, the Empire is generally good morally, by medieval standards (there are still torture rooms
). They do not discriminate against race, abilities, or preference, but rather welcome such factors into their ranks with little question. This differs from the generally hated Thalmor, and the commonly-criticized-Stormcloaks, who are both seen as arrogant, narrow-minded, and just flat-out racist. Hadvar and Ralof's instincts are the embodiment of this. With Hadvar: "Hear that? Stormcloaks. Maybe we can reason with them"/proposing the idea of a truce with the Stormcloaks until the dragons are dealt with; Ralof - "Can't wait to kill another Imperial!"/"It's the Imperials! Take cover!"
3. The Empire is the best option for a defeated Dominion - Honestly, anyone who believes that Skyrim alone can defeat the whole of the Aldmeri Dominion in a war is, to say the least, naive. Steel Warhammers and armor made out of cloth and chainmail will not protect Stormcloak soldiers against magic, better trained warriors, the better equipment said warriors have (including weapons and armor), or the general vast amount of legions that outnumber their own. Ulfric plans to attack the Thalmor immediately after liberating Skyrim (and, as brought up by DrunkenMage, they have no way to get there in full force anyway), which is insanely idiotic, and even if he played it defensively, they would eventually be invaded (with minimal to moderate difficulty). However, that is assuming the following: a. the Dominion defeats the Empire. b. They don't all starve to death. c. Hammerfell has no interest in attacking (Again, as DrunkenMage said, it would be likely, according to lore, for Hammerfell to attempt to invade Skyrim; however, I am unsure of how that war would play out).
4. Short-term, and long-term, the Empire is most beneficial - As previously stated, an independent Skyrim would not last long. The fact that you now have headstrong warriors thumping their chests over reasonable, caring, and intelligent Jarls (excluding Black-Briar and Siddgeir; I actually prefer their Stormcloak counterparts) doesn't make it better.